An unsteady flow can dramatically enhance the mixing efficiency in a highly localized region, as the flow would become chaotic if time is an independent variable. In this work, the response of uniform electroosmotic flow to an oscillating electric field is first examined experimentally and numerically as a function of the driving frequency. Then a steady in-plane micro vortex flow pattern, traced by microparticles, is realized and compared to numerical simulations. Upon confirmation of the simulations for uniform but unsteady and steady but non-uniform flows, the CFD code has finally been applied to study unsteady non-uniform flow field, for which it is difficult to measure flow properties. The time evolution of liquid vortex motion in a microchannel, due to either sinusoidal or sudden electric field reversal, is numerically investigated revealing the relationship between length and time scales dominating momentum transfer in electrokinetically-driven unsteady liquid flow.